Question

http://gyazo.com/76120b911a1d59109d22280453246bcf

1. Rewrite the constraints in slope-intercept form.



2. List all vertices of the feasible region as ordered pairs.



3. List the values of the objective function for each vertex.



4. List the maximum or minimum amount, including the x, and y-value, of the objective
function.

I do have a graphic calculator I can use if I know what to put into it. But I don't, right now.


@e.mccormick

Answer 1

OK. The whole reason they want them in slope intercept form is for use with a graphing calculator. If you have one or not, they probably want it in that form as part of the answer.

Answer 2

Okay.

Answer 3

Once you have it in that form, you graph it. Now, the graph will have some sort of overlapping area. that overlapping area will have corners.

Answer 4

Okay, how do I get it into that form?

Answer 5

The corners are the vertices.

Each one will have an (x,y) coordinate.

Answer 6

The slope/intercept form? Solve for y.

Answer 7

ax+by=c
ax-ax+by=c-ax
by=c-ax
b/b y=(c-ax)/b
y=c/b - (ax)/b

That sort of thing. But with some of thsoe being \(\le \ge\) you need to be careful if you divide by a negative.

Answer 8

..Uhm..Okay.

Answer 9

We;;, lets look at the example problem.

\(-3x+2y\le 8\)

\(-3x+3x+2y\le 8+3x\)

\(\cancel{-3x+3x}+2y\le 8+3x\)

\(2y\le 8+3x\)

\(\dfrac{2y}{2}\le \dfrac{8+3x}{2}\)

\(\dfrac{\cancel 2y}{\cancel 2}\le \dfrac{8}{2}+\dfrac{3x}{2}\)

\(y\le 4+\dfrac{3}{2}x\)

That is slope intercept form.

Answer 10

Oh! I got it now, thanks.

Answer 11

Then there is graphing it. If you have a graphing calculator, great. Otherwise:
https://www.desmos.com/calculator/yhsi3jaigo

Now, I only graphed the first two. Why? Because \(x\ge 0\) and \(y\ge 0\) just mean it is in the first quadrent! If those had been say \(x\ge 3\) then I would have also graphed them.

Answer 12

Okay!

Answer 13

Now, if you look at the overlap of red and blue, they have four corners they share that are in the first quadrent. (0,0), (6,0), (8,16), and (0,4).

Answer 14

Okay.

Answer 15

There is that formula, P=13x+2y. Well, for each point you get, you put it in. These are (x,y) points, so (6,0) becomes P=13(0)+2(6)
P=13(0)+2(6)
P=0+12
P=12

You do all four points.

Then, if you are asked for the maximum, you give the highest value. Minimum, the lowest.

Answer 16

So the highest and the minimum values would be the answers from the formula?

Answer 17

Exactly! So on this one, the lowst is 0 at (0,0) which os pretty obvious. Buit the max might be any of the other three.

Answer 18

2. List all vertices of the feasible region as ordered pairs.



3. List the values of the objective function for each vertex
Real quick, what exactly would these be? Like, these words confuse me though I understand what you are saying

Answer 19

The ordered pairs are the (x,y) points.

The values of the objective function is what I just showed, the P= stuff.

Answer 20

Okay!

Answer 21

Thank you so much.

Answer 22

And if you get stuck, here is another reference:
http://www.youtube.com/watch?v=I7brzjFhYEU

Not quite the same method, but covers a the same topic. He does not set things to y=, which your assignment is asking for. He is using the paper graphing method, where slope/intercept does not matter.

Answer 23

Alright, I can't thank you enough.

Answer 24

np. Have fun!